1. Field of the Invention
This invention relates to an apparatus for measuring the distribution of the ultrasonic wave attenuation constant of a medium, particularly to an apparatus utilizing the center frequency shift method for measuring ultrasonic wave attenuation constant distribution on a real time basis using simple hardware and without obtaining a reflected wave spectrum.
2. Description of the Prior Art
The center frequency shift method is a known method for obtaining the attenuation constant in an ultrasonic wave medium. In this method, as illustrated in FIG. 1, the power spectrum A(f) of a transmitted ultrasonic wave has a Gaussian distribution expressed as EQU A(f)=K e.sup.-[(f-f.sbsp.o).spsp.2.sup./2 .sigma..spsp.2.sup.]( 1)
In equation (1), K is a constant, the variance .sigma. is a constant proportional to the bandwidth and dependent on the shape of the spectrum of the transmitted ultrasonic wave and f.sub.o is the center frequency. The power spectrum of the received signal A'(f) also has a Gaussian distribution which is expressed as follows where f.sub.r is the center frequency of the received signal: EQU A'(f)=K'e.sup.-[(f-f.sbsp.r).spsp.2.sup./2 .sigma..spsp.2.sup.]( 2)
If it is assumed that the attenuation within the medium has the form: ##EQU1## where z is the distance between the transmitting/receiving transducer and the reflecting surface, f is the frequency, .beta. is the attenuation slope coefficient and "4" allows for traversing the distance z twice and conversion of pressure into power, then K' and f.sub.r are defined by the following equations: ##EQU2## Therefore, the attenuation slope coefficient .beta. can be obtained in the form indicated below by detecting the center frequency f.sub.r of the received signal. EQU .beta.(z)=[1/(4.sigma..sup.2)](f.sub.o -f.sub.r) d/dz (5)
However, the received signal waveform is distorted and its spectrum deviates from a Gaussian distribution, and therefore the center frequency cannot be obtained easily. To overcome this problem, the following method has been used by the prior art to obtain the center frequency f.sub.r. The power spectrum P(f) is first obtained by a Fourier transformation of the time domain waveform of the received signal for a certain time window T, and then the average frequency f is obtained according to equation (6) as the first moment of the power spectrum. ##EQU3## The average frequency f is then used as the center frequency f.sub.r in equation (5) and a value for the attenuation slope coefficient .beta. is obtained using equation (5).
A drawback of this method is the relatively large amount of time required for calculating the power spectrum and the first moment and therefore it has been difficult to obtain the distribution of .beta. on a real time basis.